As is described in Patent Document-1, in case of to carrying out an up-shift with an accelerator pedal kept depressed by a driver (which will be referred to as power-on up-shift hereinafter), an inertia phase in which a change of gear ratio is actually made produces an inertial phase due to an engaging side clutch capacity for carrying out a speed change. While, in case of carrying out up-shift with the accelerator pedal released from the driver's foot (which will be referred to as power-off up-shift hereinafter), a control is so made as to extremely reduce an output shaft torque in the inertia phase for reducing a torque step difference (or shift shock) produced at the end of the inertia phase, because in such case an engine torque is low and thus the output shaft torque after establishing the up-shift becomes low. Accordingly, the engaging side torque capacity in the inertial phase is controlled to a very low capacity and furthermore the releasing side is forced to have a certain clutch capacity in the inertial phase, and at the end of the inertial phase, the engaging side capacity is increased while releasing the releasing side capacity. With such control, an output shaft torque at the end of the inertia phase becomes an engine coast torque, so that with production of the releasing side capacity in the inertial phase, the output shaft torque is reduced by an amount corresponding to the releasing side capacity thereby to reduce a torque step difference (shift shock) at the end of the inertial phase.